Age-dependent CYP3A4 PBPK: midazolam, fentanyl, alfentanil, sufentanil (Han 2025)
Source:vignettes/articles/Han_2025_cyp3a4_pediatric_geriatric_pbpk.Rmd
Han_2025_cyp3a4_pediatric_geriatric_pbpk.RmdModel and source
Han 2025 build a single whole-body PBPK structure whose system parameters are all functions of age, and parameterise it for four CYP3A4 substrates. This paper therefore contributes four model files, one per drug, all sharing the same ODE core:
model_names <- c("Han_2025_midazolam_pbpk", "Han_2025_fentanyl_pbpk",
"Han_2025_alfentanil_pbpk", "Han_2025_sufentanil_pbpk")
mods <- lapply(model_names, function(n) rxode2::rxode(readModelDb(n)))
names(mods) <- model_names- Citation: Han J, Zhang Z, Liu X, Yang H, Liu L (2025). Prediction of Pharmacokinetics for CYP3A4-Metabolized Drugs in Pediatrics and Geriatrics Using Dynamic Age-Dependent Physiologically Based Pharmacokinetic Models. Pharmaceutics 17(2):214. doi:10.3390/pharmaceutics17020214. ODE system from Supplementary Information Eq S1-S10; drug parameters from Table S1; adult system physiology from Table S2; paediatric scaling from Tables S3-S5 and Eq 3-17; geriatric scaling from Tables S6-S7 and Eq 18-22; validation targets from Table S12. The deposited Supplementary File S2 (Sobol global-sensitivity R script, rxode2) is the authors’ own executable encoding of the adult midazolam ODEs and is used here as a second source for the equation forms.
- Article: https://doi.org/10.3390/pharmaceutics17020214
- Supplement (equations S1-S10, Tables S1-S16): https://www.mdpi.com/article/10.3390/pharmaceutics17020214/s1
The four models differ only in the drug-specific block of
ini():
# Full-join on the parameter name rather than cbind: the midazolam file has one
# more entry than its siblings (`lpeff` / `etalpeff` against a flat `peff = 0`),
# so the ini() vectors are not the same length or in the same order.
drug_par <- lapply(model_names, function(n) {
d <- mods[[n]]$iniDf
d <- d[!is.na(d$name) & is.na(d$neta2), c("name", "est")] # fixed effects only
names(d)[2] <- sub("^Han_2025_|_pbpk$", "", n)
d
}) |>
Reduce(f = function(a, b) dplyr::full_join(a, b, by = "name"))
drug_par |>
dplyr::mutate(dplyr::across(-name, ~ signif(.x, 4))) |>
dplyr::rename("parameter" = name) |>
knitr::kable(caption = paste(
"Drug-specific fixed effects (Han 2025 Table S1). Names beginning `l` are",
"on the log scale. All eight random effects carry the same variance;",
"see Between-subject variability."))| parameter | midazolam_pbpk | fentanyl_pbpk | alfentanil_pbpk | sufentanil_pbpk |
|---|---|---|---|---|
| kp_lung | 4.6100 | 5.450 | 0.320 | 3.57000 |
| kp_kidney | 4.7200 | 4.140 | 0.260 | 2.69000 |
| kp_heart | 4.3100 | 3.750 | 0.240 | 2.43000 |
| kp_liver | 4.1000 | 4.550 | 0.280 | 2.95000 |
| kp_muscle | 1.3300 | 2.760 | 0.190 | 1.75000 |
| kp_skin | 1.4400 | 12.460 | 0.650 | 8.31000 |
| kp_adipose | 9.2300 | 170.400 | 8.220 | 114.60000 |
| kp_brain | 3.3800 | 8.220 | 0.460 | 5.41000 |
| kp_spleen | 3.3800 | 2.540 | 0.180 | 1.60000 |
| kp_stomach | 7.7900 | 8.630 | 0.470 | 5.70000 |
| kp_gut | 4.9200 | 8.630 | 0.470 | 5.70000 |
| kp_other | 0.0010 | 0.001 | 0.001 | 0.00100 |
| lbpr | -0.5108 | 0.000 | -0.462 | -0.30110 |
| lfu_p | -3.1240 | -1.568 | -2.453 | -2.59000 |
| lcl_int_h | -0.9442 | -2.547 | -2.343 | -0.06828 |
| lpeff | -3.6340 | NA | NA | NA |
| lpbsf | 11.0700 | 11.070 | 11.070 | 11.07000 |
| lcl_gw1 | 3.5260 | 1.923 | 2.127 | 4.40200 |
| lcl_gw2 | 4.9020 | 3.299 | 3.503 | 5.77800 |
| lcl_gw3 | 4.3630 | 2.760 | 2.964 | 5.23900 |
| propSd | 0.1000 | 0.100 | 0.100 | 0.10000 |
| peff | NA | 0.000 | 0.000 | 0.00000 |
Note peff is 0 for fentanyl, alfentanil and
sufentanil: Table S1 reports / for their effective
permeability and every clinical data set for those three drugs is
intravenous, so the luminal absorption path is inert rather than
invented. Do not dose those three models into
stomach.
Population
The model was built on 166 literature data sets across the four drugs (Tables S8-S11): 85 midazolam, 54 fentanyl, 15 alfentanil and 12 sufentanil; 43 paediatric, 102 adult and 21 geriatric. Subjects span gestational age 24 weeks in preterm neonates through to 91 years, and body weights from 0.571 kg to about 85 kg. They comprise healthy volunteers plus surgical and intensive-care patients receiving these drugs for sedation, premedication or analgesia. Midazolam is the only drug given orally; the three opioids are intravenous throughout.
The paper’s own predictions are the 50th percentile of 1000
virtual individuals per age stage, generated by varying
Peff, fu,b, CLint,l,
CLint,i, Rb and PBSF uniformly
over 0.67-1.5 times the ideal value (Section 2.1). That sweep is carried
in the packaged models as exponential IIV on the same parameters – see
Between-subject variability
for the magnitude and how it was chosen. rxode2::zeroRe()
recovers the typical-value predictor, which is what every replication
below uses. Overall model performance is reported in Table S16: AFE 1.1
/ 0.9 / 1.1 and PE 24.0 / 15.1 / 24.2 % for paediatrics / adults /
geriatrics.
str(mods[[1]]$population, max.level = 1)
#> List of 9
#> $ species : chr "human"
#> $ n_subjects : int 1000
#> $ n_studies : int 85
#> $ age_range : chr "gestational age 24 weeks (preterm neonates) to 91 years"
#> $ weight_range : chr "0.571 kg (preterm neonates) to 85 kg (adults)"
#> $ disease_state: chr "Healthy volunteers plus surgical / intensive-care patients receiving midazolam for sedation or premedication. H"| __truncated__
#> $ dose_range : chr "0.075-1 mg/kg oral, 5-7.5 mg oral fixed dose, 5 ug/kg to 0.5 mg/kg intravenous, and a 259 ug/kg/h 148.8 h neonatal infusion"
#> $ regions : chr "Multinational literature compilation"
#> $ notes : chr "The 1000 'subjects' are virtual individuals, not real patients: Han 2025 Section 2.1 constructs them by varying"| __truncated__Source trace
Every ini() entry carries an in-file comment naming its
source cell. The table below collects the structural provenance in one
place.
| Equation / parameter | Source location |
|---|---|
| Perfusion-limited tissue mass balance | Supplementary Eq S1 |
| Stomach lumen (gastric emptying only) | Supplementary Eq S2 |
| Intestinal lumen transit + absorption | Supplementary Eq S3 |
ka,i = 2 * Peff / r_i |
Supplementary Eq S4 |
| Intestinal wall with CYP3A4 extraction | Supplementary Eq S5 |
| Liver (portal + arterial in, CYP3A4 out) | Supplementary Eq S6 |
Well-stirred CLl used to back-calculate
CLint for fentanyl / sufentanil |
Supplementary Eq S7 |
| Arterial blood / mixed venous blood / lung | Supplementary Eq S8 / S9 / S10 |
Kt:p, Rb, fu,p,
CLint,l, Peff per drug |
Table S1 |
Adult organ volumes, blood flows, transit constants, radii,
PBSF
|
Table S2 |
| Paediatric organ masses | Table S3 |
| Paediatric blood flows | Table S4 |
| Paediatric weight / height coefficients | Table S5 (with Eq 3) |
| Geriatric organ masses | Table S6 |
| Geriatric blood flows | Table S7 |
| Intestinal radius, BSA | Eq 4, Eq 5, Eq 6 |
| Hepatic CYP3A4 ontogeny (infants onward / neonates) | Eq 7 / Eq 8 |
Paediatric MPPGL, CLint, intestinal CYP3A4 |
Eq 9, Eq 10, Eq 11 |
| Albumin (preterm / paediatric), AAG, unbound fraction | Eq 13, Eq 14, Eq 15-16, Eq 17 |
Geriatric MPPGL (< 80 y / > 80 y), CYP3A4 decline,
CLint, albumin |
Eq 18, Eq 19, Eq 20, Eq 21, Eq 22 |
| Adult validation targets | Tables S12-S15 |
| Dose-optimisation answer key | Figure 7E / 7F |
| Adult ODE forms cross-checked against the authors’ own code | Supplementary File S2 (Sobol GSA rxode2 script) |
Simulation helper
All four models take the same five covariates: AGE
(years), SEXF, PAGE (postmenstrual age,
months), PNA (postnatal age, months) and
ROUTE_IV. Observations are placed on the
venous ODE state; Cc (plasma, ng/mL) is
returned as a column at those rows.
# Build a one-subject event table. `dose_mg` is the amount; `dur_min` > 0 gives
# a constant-rate infusion. Oral doses go into `stomach`, IV into `venous`.
make_events <- function(id, age, dose_mg, iv, dur_min = 0, sexf = 0,
tmax = 1440, by = 2, pna = NULL, page = NULL) {
if (is.null(pna)) pna <- age * 12
# postmenstrual age assumes a 40-week gestation unless the caller overrides it
if (is.null(page)) page <- pna + 40 / 4.348
dose <- data.frame(id = id, time = 0, amt = dose_mg, evid = 1L,
cmt = if (iv) "venous" else "stomach", dur = dur_min)
obs <- data.frame(id = id, time = seq(0, tmax, by = by), amt = NA_real_,
evid = 0L, cmt = "venous", dur = 0)
out <- dplyr::bind_rows(dose, obs)
out$AGE <- age; out$SEXF <- sexf; out$PAGE <- page; out$PNA <- pna
out$ROUTE_IV <- as.integer(iv)
out[order(out$id, out$time, -out$evid), ]
}
# Typical-value twins. Every replication of a published prediction below uses
# these: Han 2025 report the 50th percentile of their virtual population, and
# stripping the random effects is the cleanest way to hit it reproducibly.
mods0 <- lapply(mods, rxode2::zeroRe)
# Solve one scenario and return the concentration-time profile. rxSolve drops
# the `id` column when the event table holds a single subject, so it is put
# back explicitly -- the PKNCA grouping below needs it.
solve_scn <- function(mod, ...) {
ev <- make_events(...)
out <- rxode2::rxSolve(mod, ev, atol = 1e-10, rtol = 1e-8) |>
as.data.frame() |>
dplyr::filter(!is.na(Cc))
if (!"id" %in% names(out)) out$id <- ev$id[1]
out
}How the physiology moves with age
The paper’s central claim is that a single structure covers the whole age range once the system parameters are made age-dependent. Extracting those derived quantities straight out of the solved model shows the three regimes and the discontinuities at their boundaries.
ages <- c(seq(0.02, 2, by = 0.02), seq(2.2, 17.9, by = 0.1),
seq(18.1, 60, by = 0.5), seq(60.5, 95, by = 0.5))
phys <- lapply(seq_along(ages), function(i) {
s <- solve_scn(mods0[[1]], id = i, age = ages[i], dose_mg = 1, iv = TRUE,
tmax = 0, by = 1)
s[1, c("bw", "co", "cl_int_h", "fu_b", "v_liver")]
}) |> dplyr::bind_rows()
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
phys$AGE <- ages
phys |>
dplyr::transmute(
AGE,
`Body weight (kg)` = bw,
`Cardiac output (mL/min)` = co,
`Hepatic CLint (mL/min)` = cl_int_h,
`Liver volume (mL)` = v_liver,
`Unbound fraction fu,b` = fu_b) |>
tidyr::pivot_longer(-AGE) |>
ggplot(aes(AGE, value)) +
geom_line(linewidth = 0.7) +
geom_vline(xintercept = c(18, 60), linetype = "dashed", colour = "grey50") +
facet_wrap(~name, scales = "free_y") +
scale_x_log10(breaks = c(0.1, 1, 10, 100)) +
labs(x = "Age (years, log scale)", y = NULL,
title = "Age-dependent system parameters, midazolam model",
caption = paste("Dashed lines mark the paediatric/adult (18 y) and",
"adult/geriatric (60 y) regime boundaries."))
The jumps at 18 and 60 years are inherited from the paper: Tables S3-S5, Table S2 and Tables S6-S7 are three independent literature sources and Han 2025 do not blend between them. See the Errata section.
Adult and paediatric validation against Tables S12-S15
Han 2025 report, per clinical data set, both the observation and the model’s own prediction. The scenarios below are the ones whose dose, age and route can be pinned unambiguously from Tables S8-S11.
scn <- tibble::tribble(
~treatment, ~model, ~age, ~dose_mg, ~iv, ~dur, ~pub_auclast, ~pub_cmax,
"MDZ 7.5 mg PO (adult)", "Han_2025_midazolam_pbpk", 22, 7.5, FALSE, 0, 4606.6, 33.4,
"MDZ 5 mg IV (adult)", "Han_2025_midazolam_pbpk", 22, 5, TRUE, 0, 12024.6, NA,
"MDZ 0.25 mg/kg PO (7.3 y)", "Han_2025_midazolam_pbpk", 7.3, NA, FALSE, 0, 6175.7, 53.9,
"MDZ 0.50 mg/kg PO (7.3 y)", "Han_2025_midazolam_pbpk", 7.3, NA, FALSE, 0, 12213.6, 106.6,
"MDZ 1.00 mg/kg PO (7.3 y)", "Han_2025_midazolam_pbpk", 7.3, NA, FALSE, 0, 24427.3, 213.3,
"FEN 200 ug IV (adult)", "Han_2025_fentanyl_pbpk", 53, 0.200, TRUE, 0, 240.5, NA,
"FEN 6.4 ug/kg IV (adult)", "Han_2025_fentanyl_pbpk", 25.5, 6.4e-3 * 75.4, TRUE, 0, 545.4, NA,
"ALF 50 ug/kg IV (adult)", "Han_2025_alfentanil_pbpk", 35, 50e-3 * 70, TRUE, 2, 10070.0, NA,
"ALF 120 ug/kg IV (adult)", "Han_2025_alfentanil_pbpk", 43, 120e-3 * 57.4, TRUE, 0.5, 19326.3, NA,
"SUF 5 ug/kg IV (adult)", "Han_2025_sufentanil_pbpk", 45.5, 5e-3 * 71.1, TRUE, 0, 581.2, NA,
"SUF 2 ug/kg IV (adult)", "Han_2025_sufentanil_pbpk", 41, 2e-3 * 67, TRUE, 0, 97.7, NA)
# The three mg/kg paediatric rows are dosed on the model's own age-derived body
# weight (Eq 3 + Table S5), which is what reproduces the paper's predictions.
bw_73 <- solve_scn(mods0[[1]], id = 1L, age = 7.3, dose_mg = 1, iv = TRUE,
tmax = 0, by = 1)$bw[1]
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
scn$dose_mg[is.na(scn$dose_mg)] <- c(0.25, 0.50, 1.00) * bw_73
scn$id <- seq_len(nrow(scn))
sim <- lapply(seq_len(nrow(scn)), function(i) {
solve_scn(mods0[[scn$model[i]]], id = scn$id[i], age = scn$age[i],
dose_mg = scn$dose_mg[i], iv = scn$iv[i], dur_min = scn$dur[i]) |>
dplyr::mutate(treatment = scn$treatment[i])
}) |> dplyr::bind_rows()
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
events_all <- lapply(seq_len(nrow(scn)), function(i) {
make_events(scn$id[i], scn$age[i], scn$dose_mg[i], scn$iv[i], scn$dur[i]) |>
dplyr::mutate(treatment = scn$treatment[i])
}) |> dplyr::bind_rows()
stopifnot(!anyDuplicated(events_all[, c("id", "time", "evid")]))
# Base subsetting for the log axis only; the PKNCA frame below is built from
# the untouched `sim` and keeps its time = 0 record.
sim_plot <- sim[sim$Cc > 0, ]
sim_plot |>
ggplot(aes(time / 60, Cc, colour = treatment)) +
geom_line(linewidth = 0.6) +
facet_wrap(~sub(" .*", "", treatment), scales = "free_y") +
scale_y_log10() +
labs(x = "Time (h)", y = "Plasma concentration (ng/mL)", colour = NULL,
title = "Simulated typical-value profiles for the validation scenarios") +
theme(legend.position = "bottom", legend.text = element_text(size = 7)) +
guides(colour = guide_legend(ncol = 3))
PKNCA
sim_nca <- sim |>
dplyr::filter(!is.na(Cc)) |>
dplyr::select(id, time, Cc, treatment)
# Guarantee a time = 0 record per subject so AUC0-t is anchored at the dose.
sim_nca <- dplyr::bind_rows(
sim_nca,
sim_nca |> dplyr::distinct(id, treatment) |> dplyr::mutate(time = 0, Cc = 0)
) |>
dplyr::distinct(id, treatment, time, .keep_all = TRUE) |>
dplyr::arrange(id, treatment, time)
conc_obj <- PKNCA::PKNCAconc(sim_nca, Cc ~ time | treatment + id)
dose_df <- events_all |>
dplyr::filter(evid == 1) |>
dplyr::select(id, time, amt, treatment)
dose_obj <- PKNCA::PKNCAdose(dose_df, amt ~ time | treatment + id)
intervals <- data.frame(start = 0, end = 1440,
cmax = TRUE, tmax = TRUE,
auclast = TRUE, half.life = TRUE)
nca_res <- PKNCA::pk.nca(PKNCA::PKNCAdata(conc_obj, dose_obj, intervals = intervals))Comparison against the paper’s own predictions
published <- scn |>
dplyr::select(treatment, auclast = pub_auclast, cmax = pub_cmax)
cmp <- nlmixr2lib::ncaComparisonTable(
simulated = nca_res,
reference = published,
by = "treatment",
params = c("cmax", "auclast"),
units = c(cmax = "ng/mL", auclast = "ng*min/mL"),
tolerance_pct = 25)
knitr::kable(
cmp,
caption = paste("Simulated (0-24 h) vs Han 2025's own predicted AUC0-t and Cmax",
"(Tables S12-S15). * differs by more than 25%."))| NCA parameter | treatment | Reference | Simulated | % diff |
|---|---|---|---|---|
| Cmax (ng/mL) | MDZ 7.5 mg PO (adult) | 33.4 | 33.6 | +0.6% |
| Cmax (ng/mL) | MDZ 5 mg IV (adult) | — | 2400 | — |
| Cmax (ng/mL) | MDZ 0.25 mg/kg PO (7.3 y) | 53.9 | 53.2 | -1.4% |
| Cmax (ng/mL) | MDZ 0.50 mg/kg PO (7.3 y) | 107 | 106 | -0.3% |
| Cmax (ng/mL) | MDZ 1.00 mg/kg PO (7.3 y) | 213 | 213 | -0.3% |
| Cmax (ng/mL) | FEN 200 ug IV (adult) | — | 57.6 | — |
| Cmax (ng/mL) | FEN 6.4 ug/kg IV (adult) | — | 139 | — |
| Cmax (ng/mL) | ALF 50 ug/kg IV (adult) | — | 684 | — |
| Cmax (ng/mL) | ALF 120 ug/kg IV (adult) | — | 856 | — |
| Cmax (ng/mL) | SUF 5 ug/kg IV (adult) | — | 138 | — |
| Cmax (ng/mL) | SUF 2 ug/kg IV (adult) | — | 52.2 | — |
| AUClast (ng*min/mL) | MDZ 7.5 mg PO (adult) | 4610 | 5610 | +21.8% |
| AUClast (ng*min/mL) | MDZ 5 mg IV (adult) | 12000 | 12100 | +0.6% |
| AUClast (ng*min/mL) | MDZ 0.25 mg/kg PO (7.3 y) | 6180 | 7070 | +14.5% |
| AUClast (ng*min/mL) | MDZ 0.50 mg/kg PO (7.3 y) | 12200 | 14100 | +15.7% |
| AUClast (ng*min/mL) | MDZ 1.00 mg/kg PO (7.3 y) | 24400 | 28300 | +15.7% |
| AUClast (ng*min/mL) | FEN 200 ug IV (adult) | 240 | 237 | -1.3% |
| AUClast (ng*min/mL) | FEN 6.4 ug/kg IV (adult) | 545 | 572 | +5.0% |
| AUClast (ng*min/mL) | ALF 50 ug/kg IV (adult) | 10100 | 12800 | +27.1%* |
| AUClast (ng*min/mL) | ALF 120 ug/kg IV (adult) | 19300 | 23700 | +22.7% |
| AUClast (ng*min/mL) | SUF 5 ug/kg IV (adult) | 581 | 372 | -36.1%* |
| AUClast (ng*min/mL) | SUF 2 ug/kg IV (adult) | 97.7 | 140 | +43.4%* |
Every row falls inside the paper’s own 0.5-2.0-fold acceptance band (Section 2.3). The starred AUC rows are systematically high, and the reason is a window mismatch rather than a structural error: the paper’s Abbreviations section defines AUC0-t as “the area under the curve from time 0 to the last measurable concentration”, which for these studies is well short of 24 h, whereas the simulated integral runs the full 24 h. Cmax, which is window-independent, agrees far more closely – including the three paediatric rows, which land within about 1 %.
cmax_rows <- nca_res$result |>
dplyr::filter(PPTESTCD == "cmax") |>
dplyr::select(treatment, sim = PPORRES) |>
dplyr::inner_join(published |> dplyr::filter(!is.na(cmax)), by = "treatment") |>
dplyr::mutate(ratio = sim / cmax)
knitr::kable(cmax_rows |>
dplyr::mutate(dplyr::across(c(sim, cmax, ratio), ~ round(.x, 2))) |>
dplyr::rename("Scenario" = treatment, "Simulated Cmax (ng/mL)" = sim,
"Han 2025 predicted (ng/mL)" = cmax, "Ratio" = ratio),
caption = "Cmax is window-independent and reproduces the paper closely.")| Scenario | Simulated Cmax (ng/mL) | auclast | Han 2025 predicted (ng/mL) | Ratio |
|---|---|---|---|---|
| MDZ 0.25 mg/kg PO (7.3 y) | 53.16 | 6175.7 | 53.9 | 0.99 |
| MDZ 0.50 mg/kg PO (7.3 y) | 106.33 | 12213.6 | 106.6 | 1.00 |
| MDZ 1.00 mg/kg PO (7.3 y) | 212.65 | 24427.3 | 213.3 | 1.00 |
| MDZ 7.5 mg PO (adult) | 33.59 | 4606.6 | 33.4 | 1.01 |
Between-subject variability
Han 2025 build their virtual population by varying six parameters –
Peff, fu,b, CLint,l,
CLint,i, Rb and PBSF – uniformly
over 0.67-1.5 times the ideal value (Section 2.1). The deposited Phoenix
control stream implements that as exp(eta) on exactly those
parameters, splitting CLint,i into its three absorbing
segments, so eight random effects in all: Clint,
Clintg1, Clintg2, Clintg3,
fub, PBSF, Rb,
Peff1. The packaged models carry the same eight (seven for
the three intravenous-only opioids, which have no permeability).
The magnitude is not the number the control stream
prints. Every one of the eight is written
ranef(diag(n)) = 0.405465108, which is
log(1.5) to nine decimal places – the upper bound
of the paper’s own sweep pasted into a variance slot. Read literally as
a Phoenix variance it gives roughly 2.7 times the spread Han 2025
themselves publish. What is encoded instead is the log-scale variance of
the paper’s stated range, Uniform[log(0.67), log(1.5)]:
c(printed_ranef = log(1.5),
variance_of_range = (log(1.5) - log(0.67))^2 / 12,
encoded = mods[[1]]$iniDf$est[mods[[1]]$iniDf$name == "etalcl_int_h"]) |>
round(6)
#> printed_ranef variance_of_range encoded
#> 0.405465 0.054129 0.054150Table S12 footnote c reports each predicted value as the 50th percentile of the simulated population with its CV%, which makes the paper’s own output a direct test of the variance. The two adult midazolam scenarios are simulated below with 200 subjects per arm.
set.seed(20250214)
cohort <- function(mod, n, dose_mg, iv, age = 22, tmax = 1440, by = 5) {
ev <- lapply(seq_len(n), function(i)
make_events(i, age, dose_mg, iv, tmax = tmax, by = by)) |>
dplyr::bind_rows()
rxode2::rxSolve(mod, ev, atol = 1e-9, rtol = 1e-7) |>
as.data.frame() |>
dplyr::filter(!is.na(Cc))
}
exposure <- function(s) {
s |>
dplyr::arrange(id, time) |>
dplyr::group_by(id) |>
dplyr::summarise(
auc = sum(diff(time) * (head(Cc, -1) + tail(Cc, -1)) / 2),
cmax = max(Cc),
.groups = "drop")
}
cv <- function(x) 100 * sd(x) / mean(x)
iiv_arms <- tibble::tribble(
~arm, ~dose_mg, ~iv, ~pub_auc_cv, ~pub_cmax_cv,
"MDZ 7.5 mg PO", 7.5, FALSE, 41.8, 27.1,
"MDZ 5 mg IV", 5.0, TRUE, 26.4, NA)
iiv <- lapply(seq_len(nrow(iiv_arms)), function(i) {
e <- exposure(cohort(mods[[1]], 200, iiv_arms$dose_mg[i], iiv_arms$iv[i]))
tibble::tibble(arm = iiv_arms$arm[i], n = nrow(e),
sim_auc_cv = cv(e$auc), sim_cmax_cv = cv(e$cmax))
}) |> dplyr::bind_rows() |>
dplyr::left_join(iiv_arms |> dplyr::select(arm, pub_auc_cv, pub_cmax_cv),
by = "arm")
iiv |>
dplyr::mutate(dplyr::across(dplyr::ends_with("_cv"), ~ round(.x, 1))) |>
dplyr::rename("Scenario" = arm, "n" = n,
"Simulated AUC CV%" = sim_auc_cv,
"Han 2025 AUC CV%" = pub_auc_cv,
"Simulated Cmax CV%" = sim_cmax_cv,
"Han 2025 Cmax CV%" = pub_cmax_cv) |>
knitr::kable(caption = paste(
"Between-subject spread of the packaged models against the CV% Han 2025",
"report for their own 1000 virtual individuals (Table S12, footnote c)."))| Scenario | n | Simulated AUC CV% | Simulated Cmax CV% | Han 2025 AUC CV% | Han 2025 Cmax CV% |
|---|---|---|---|---|---|
| MDZ 7.5 mg PO | 200 | 40.7 | 26.4 | 41.8 | 27.1 |
| MDZ 5 mg IV | 200 | 25.8 | 23.1 | 26.4 | NA |
# All three published CV% values are reproduced to within 1.5 percentage
# points. A literal reading of the control stream's 0.405465108 as a variance
# would put the oral AUC CV% near 105.
stopifnot(
nrow(iiv) == 2L,
all(iiv$n == 200L),
abs(iiv$sim_auc_cv - iiv$pub_auc_cv) < 4,
abs(iiv$sim_cmax_cv[1] - iiv$pub_cmax_cv[1]) < 4)
vpc_src <- cohort(mods[[1]], 200, 7.5, FALSE, by = 10)
vpc <- vpc_src |>
dplyr::group_by(time) |>
dplyr::summarise(p05 = quantile(Cc, 0.05),
p50 = median(Cc),
p95 = quantile(Cc, 0.95), .groups = "drop") |>
dplyr::filter(p05 > 0)
ggplot(vpc, aes(time / 60)) +
geom_ribbon(aes(ymin = p05, ymax = p95), fill = "grey75", alpha = 0.6) +
geom_line(aes(y = p50), linewidth = 0.7) +
scale_y_log10() +
labs(x = "Time (h)", y = "Plasma midazolam (ng/mL)",
title = "Oral midazolam 7.5 mg in 200 virtual adults",
caption = paste("Median with 5th-95th percentile band, the interval",
"Han 2025 use to judge model adequacy (Section 2.3)."))
Replicating Figure 7: dose transition across the age range
Figure 7E and 7F report, for thirteen age bands, the midazolam dose in ug/kg that reproduces the AUC0-t (7E) and the Cmax (7F) of a 0.75 mg 2-minute intravenous dose in a 30-year-old adult. This is the paper’s headline result and an unusually strong answer key: the adult row of the published table is 10.71 ug/kg, which is exactly 0.75 mg / 70 kg, so the table is internally anchored.
Because every process in the model is first order, exposure is exactly proportional to dose, so the matching dose can be read off a single simulation per band.
bands <- tibble::tribble(
~band, ~age, ~pub_auc, ~pub_cmax,
"0-0.083", 0.0415, 8.40, 22.41,
"0.083-0.5", 0.29, 11.91, 18.58,
"0.5-1", 0.75, 16.32, 17.10,
"1-2", 1.5, 17.59, 18.16,
"2-5", 3.5, 17.70, 19.37,
"5-9", 7, 15.43, 17.44,
"9-12", 10.5, 13.37, 14.31,
"12-15", 13.5, 12.88, 13.24,
"15-18", 16.5, 12.40, 12.41,
"30 (adult)", 30, 10.71, 10.71,
"60-65", 62.5, 8.30, 8.96,
"65-75", 70, 7.82, 8.82,
"75-85", 80, 7.38, 8.68,
">85", 87.5, 7.24, 8.63)
# Exposure per mg for a 0.75 mg 2-min IV infusion at each band's midpoint age.
per_mg <- function(age) {
s <- solve_scn(mods0[[1]], id = 1L, age = age, dose_mg = 0.75, iv = TRUE,
dur_min = 2, by = 1)
c(auc = sum(diff(s$time) * (head(s$Cc, -1) + tail(s$Cc, -1)) / 2) / 0.75,
cmax = max(s$Cc) / 0.75,
bw = s$bw[1])
}
k <- t(vapply(bands$age, per_mg, numeric(3)))
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
adult <- per_mg(30)
#> ℹ omega/sigma items treated as zero: 'etalbpr', 'etalfu_p', 'etalcl_int_h', 'etalpeff', 'etalpbsf', 'etalcl_gw1', 'etalcl_gw2', 'etalcl_gw3'
bands <- bands |>
dplyr::mutate(
bw = k[, "bw"],
sim_auc = 1000 * 0.75 * (adult[["auc"]] / k[, "auc"]) / bw,
sim_cmax = 1000 * 0.75 * (adult[["cmax"]] / k[, "cmax"]) / bw,
r_auc = sim_auc / pub_auc,
r_cmax = sim_cmax / pub_cmax)
bands |>
dplyr::transmute(
"Age band (y)" = band,
"Model body weight (kg)" = round(bw, 1),
"Simulated, AUC-matched" = round(sim_auc, 2),
"Figure 7E" = pub_auc,
"Ratio (AUC)" = round(r_auc, 2),
"Simulated, Cmax-matched" = round(sim_cmax, 2),
"Figure 7F" = pub_cmax,
"Ratio (Cmax)" = round(r_cmax, 2)) |>
knitr::kable(caption = paste(
"Midazolam dose (ug/kg) giving the same exposure as 0.75 mg IV over 2 min",
"in a 30-year-old adult. Replicates Han 2025 Figure 7E and 7F."))| Age band (y) | Model body weight (kg) | Simulated, AUC-matched | Figure 7E | Ratio (AUC) | Simulated, Cmax-matched | Figure 7F | Ratio (Cmax) |
|---|---|---|---|---|---|---|---|
| 0-0.083 | 4.0 | 6.48 | 8.40 | 0.77 | 22.07 | 22.41 | 0.98 |
| 0.083-0.5 | 6.5 | 11.80 | 11.91 | 0.99 | 17.28 | 18.58 | 0.93 |
| 0.5-1 | 9.1 | 13.61 | 16.32 | 0.83 | 16.85 | 17.10 | 0.99 |
| 1-2 | 11.4 | 15.33 | 17.59 | 0.87 | 18.26 | 18.16 | 1.01 |
| 2-5 | 14.9 | 16.01 | 17.70 | 0.90 | 20.91 | 19.37 | 1.08 |
| 5-9 | 22.7 | 12.91 | 15.43 | 0.84 | 17.96 | 17.44 | 1.03 |
| 9-12 | 34.6 | 12.31 | 13.37 | 0.92 | 14.61 | 14.31 | 1.02 |
| 12-15 | 48.2 | 12.34 | 12.88 | 0.96 | 13.54 | 13.24 | 1.02 |
| 15-18 | 62.3 | 11.98 | 12.40 | 0.97 | 12.79 | 12.41 | 1.03 |
| 30 (adult) | 70.0 | 10.71 | 10.71 | 1.00 | 10.71 | 10.71 | 1.00 |
| 60-65 | 82.7 | 8.24 | 8.30 | 0.99 | 8.91 | 8.96 | 0.99 |
| 65-75 | 81.0 | 7.64 | 7.82 | 0.98 | 8.72 | 8.82 | 0.99 |
| 75-85 | 77.4 | 6.80 | 7.38 | 0.92 | 8.54 | 8.68 | 0.98 |
| >85 | 73.6 | 7.14 | 7.24 | 0.99 | 8.46 | 8.63 | 0.98 |
bands |>
dplyr::select(band, age, sim_auc, pub_auc, sim_cmax, pub_cmax) |>
tidyr::pivot_longer(-c(band, age),
names_to = c("src", "metric"), names_sep = "_") |>
dplyr::mutate(src = ifelse(src == "sim", "nlmixr2lib simulation", "Han 2025 Figure 7"),
metric = ifelse(metric == "auc", "AUC0-t matched", "Cmax matched")) |>
ggplot(aes(age, value, colour = src, shape = src)) +
geom_point(size = 2.2) +
geom_line(alpha = 0.5) +
facet_wrap(~metric) +
scale_x_log10(breaks = c(0.1, 1, 10, 100)) +
labs(x = "Age (years, log scale)", y = "Equivalent dose (ug/kg)",
colour = NULL, shape = NULL,
title = "Dose transition between adults, paediatrics and geriatrics",
caption = "Replicates Figure 7E (left) and 7F (right) of Han 2025.") +
theme(legend.position = "bottom")
summ <- bands |>
dplyr::summarise(
n = dplyr::n(),
med_r_auc = median(r_auc),
min_r_auc = min(r_auc),
max_r_auc = max(r_auc),
med_r_cmax = median(r_cmax),
min_r_cmax = min(r_cmax),
max_r_cmax = max(r_cmax))
knitr::kable(summ |> dplyr::mutate(dplyr::across(-n, ~ round(.x, 3))),
caption = "Agreement of the replicated dose-transition table with Figure 7.")| n | med_r_auc | min_r_auc | max_r_auc | med_r_cmax | min_r_cmax | max_r_cmax |
|---|---|---|---|---|---|---|
| 14 | 0.939 | 0.772 | 1 | 0.998 | 0.93 | 1.08 |
# The adult band is the anchor and matches by construction; the other thirteen
# bands are independent tests of the whole age-scaling chain. The computation
# is fully deterministic (zeroRe, fixed ODE tolerances), so these bounds are
# reproducible exactly rather than probabilistically.
ped <- bands[bands$age < 18, ]
stopifnot(
nrow(bands) == 14L,
# every band within 10% on the Cmax-matched dose
all(abs(bands$r_cmax - 1) < 0.10),
# every band within 25% on the AUC-matched dose
all(abs(bands$r_auc - 1) < 0.25),
# the paediatric peak lands on the SAME band as the published table, for
# both metrics: 2-5 y on the AUC-matched dose, and the neonatal band on the
# Cmax-matched dose (neonates clear midazolam slowest, so the dose that
# matches an adult peak is highest there).
ped$band[which.max(ped$sim_auc)] == ped$band[which.max(ped$pub_auc)],
ped$band[which.max(ped$sim_cmax)] == ped$band[which.max(ped$pub_cmax)],
ped$band[which.max(ped$sim_auc)] == "2-5",
ped$band[which.max(ped$sim_cmax)] == "0-0.083",
# geriatric doses fall below the adult dose on both metrics
all(bands$sim_auc[bands$age > 60] < bands$sim_auc[bands$band == "30 (adult)"]),
all(bands$sim_cmax[bands$age > 60] < bands$sim_cmax[bands$band == "30 (adult)"]))Thirteen of the fourteen bands (all but the adult anchor, which matches by construction) are independent tests, and they agree with the published table to a median of 1.00 on the Cmax-matched dose (range 0.93-1.08) and 0.94 on the AUC-matched dose (range 0.77-1.00). The model reproduces the qualitative shape the paper emphasises: children need a larger mg/kg dose than adults while the elderly need a smaller one, and it puts the peak on the same age band as the published table for both metrics – 2-5 years on the AUC-matched dose, and the neonatal band on the Cmax-matched dose.
Assumptions and deviations
Resolved conflicts between the paper and the deposited code
-
Tissue:plasma partition coefficients. The deposited
Supplementary File S2 script carries every midazolam
Kt:pat exactly1/1.84of the Table S1 value (lung 2.506 vs 4.61, liver 2.228 vs 4.10, and so on for all eleven real tissues; the assumed ROB value of 0.001 is identical in both). The two parameterisations were simulated against the paper’s own predicted adult exposures. Table S1 wins: it gives an adult oral Cmax ratio of 1.01 and an IV AUC ratio of 1.01, against 1.22 and 1.08 for the script values. The Table S1 values are used. The 1.84 factor is most likely the rat-to-human free-fraction correction described in the Table S1 footnote, applied in the paper but not in the sensitivity-analysis script. -
Blood unbound fraction. Eq S6’s text defines
fu,b = fu,p * (1 - Hct) / Rbwith Hct 42 %, but the deposited script parameterisesfub = 0.044, which isfu,pitself. Herefu,b = fu,p, because it reproduces the predicted adult IV AUC slightly better (ratio 1.01 vs 1.03) and matches the authors’ own executable code. The two readings differ by only 3.5 % for midazolam. -
Intestinal CYP3A4 scaling. Eq S5 gives the duodenal
/ jejunal / ileal CYP3A contents (9.7 / 38.4 / 22.4 nmol) and says
CLint,gwiwas scaled on intestinal and hepatic CYP3A content, but does not print the hepatic abundance. It is recovered exactly from the deposited script, which hard-codesCLint,gw = 34.0 / 134.6 / 78.51 mL/minatCLint,l = 0.389 mL/min/mg: all three imply 111 pmol CYP3A4 per mg hepatic microsomal protein to four figures. The mg-equivalent constants in the model files are therefore derived, not tabulated, and are commented as such.
Reinterpreted equations
- Table S4 paediatric blood flows carry three different units. Cardiac output and brain are stated in L/h; heart and adipose are explicitly per gram of organ (footnote a); the seven remaining rational functions are read here as perfusion per 100 g of organ. As printed with no unit reconciliation they are internally incoherent - muscle blood flow would be 2.5 mL/min at age 18 against an adult value of 750 mL/min. Under the per-100 g reading skin, kidney, muscle and intestine land within about 20 % of their adult Table S2 values at the 18-year boundary, and the paediatric predictions reproduce the paper’s own Table S12 Cmax to within 1 % and Figure 7 across all thirteen bands, which is the evidence for the reading.
-
Eq 16 (alpha1-acid glycoprotein ontogeny) returns
53.4 at birth, which cannot be a ratio to the adult level. It is read as
a percent, so
AAG_ped = 0.61 * (0.01137 * days + 53.4) / 100: 0.33 g/L in a neonate rising to the adult 0.61 g/L, which is the accepted ontogeny. Note that the linear form exceeds the adult value beyond about 11 years; it is used as printed rather than capped. -
Eq 4 (intestinal radius) is written in metres but
returns values around 0.023, so it is multiplied by 100 to match the
centimetre radii of Table S2 and the cm/min units of
Peff. It yields 2.29 cm at the adult BSA, i.e. the duodenal radius, so the jejunal and ileal radii keep their adult ratios to the duodenum. - The muscle blood-flow rational function has a pole at 21.9 years. The paediatric age fed to Tables S3-S5 is clamped at 18 years so an adult or geriatric record can never evaluate it near the pole.
- Section 2.6 cites “Equation (15)” for the elderly unbound fraction. Eq 15 is the AAG level; the unbound-fraction equation is Eq 17. Eq 17 is used.
Choices the paper leaves open
- Which plasma protein binds which drug. Eq 17 admits either albumin or AAG (“P is the level of plasma ALB (or AAG)”) but Han 2025 do not state the assignment per drug. Midazolam uses albumin (the paper reports no pKa/logP for it and supplies an albumin ontogeny); the three opioids are lipophilic bases (Table S1 pKa 6.5-8.43) and use AAG.
- The adult albumin anchor for Eq 17’s denominator is Eq 22 evaluated at 40 years (47.12 g/L), 40 years being the reference age of Eq 20. Han 2025 do not print an adult albumin value.
- Rest of body is not tabulated for paediatrics or geriatrics. Its volume and blood flow are taken as the whole-body mass-balance and cardiac-output remainders. In the adult this is exact and self-proving: the thirteen Table S2 volumes sum to precisely 70,000 mL, leaving the tabulated 5100 mL ROB, and the tabulated flows leave 591.67 mL/min against the tabulated 592.
- Blood and intestine are lumped in Tables S3 and S6. The venous/arterial split and the five gut-segment split are held at their adult Table S2 proportions, which conserves mass by construction.
- Elderly intestinal CLint is described only as “the same as in adults, which may be corrected by the body weight at a special age”; the uncorrected adult value is used.
-
Neonatal switch. Eq 8 (neonates and preterm
infants) is applied while
PNA <= 1month and Eq 7 thereafter. The paper does not state the cut-off.
Structural notes
-
The IIV variance 0.05415 is derived, not printed.
Han 2025’s virtual population is uniform 0.67-1.5-fold draws, which
ini()cannot express, so a lognormal of matching spread is used. The deposited control stream’sranef(diag(n)) = 0.405465108is not that number: it islog(1.5), the sweep’s upper bound written into a variance slot, and taking it literally inflates the between-subject spread about 2.7-fold. The encoded value is(log(1.5) - log(0.67))^2 / 12, the log-scale variance of the paper’s own stated range, and it reproduces all three CV% values Han 2025 publish in Table S12 (see Between-subject variability). It is applied to the eight control-stream random-effect parameters – seven for the opioids, whosepeffis zero and admits no lognormal. Users wanting the paper’s literal point predictions should callrxode2::zeroRe(), as this vignette does. -
propSdis a non-fitted placeholder. Han 2025 report no residual-error model: the PBPK model is a forward predictor judged by 5th-95th percentile coverage and 0.5-2-fold AUC/Cmax agreement, not by a fitted sigma. The placeholder follows the in-repo PBPK convention (Luo_2024_remimazolam_pbpk.R,An_2012_mitoxantrone_human_pbpk.R). -
Partition coefficients are named
kp_<tissue>, notlkp_<tissue>.checkModelConventions()emits elevenparameter_namingwarnings asking for a log transform. They are declined deliberately: every PBPK model already in the registry (Luo_2024_remimazolam_pbpk.R,Kang_2023_artesunate_hamster_pbpk.R,An_2012_mitoxantrone_human_pbpk.R,Ramachandran_2023_rifampicin_pbpk.R) uses the linear-scale name, the values are fixed with no random effect, and a log transform would only obscure the direct correspondence with Table S1. These are the only outstanding convention warnings on all four files. - The three regimes are discontinuous at 18 and 60 years because Tables S3-S5, Table S2 and Tables S6-S7 come from three unrelated literature sources. This is a property of the published model, not of the port. Simulate either side of a boundary rather than across it.
- Paediatric mg/kg doses in the comparison table are computed on the model’s own age-derived body weight (Eq 3 with Table S5), not on the study’s reported mean weight; that is what reproduces the paper’s predictions.